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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Direct production of three entangled fields at different wavelengths

A. S. Coelho, F. A. S. Barbosa, J. E. S. César, K. N. Cassemiro, Alessandro S. Villar, M. Martinelli, P. Nussenzveig

Published Jun 1, 2009• 0 citations
Publisher

Abstract

This paper demonstrates the nonlinear system of the smallest order for direct tripartite entanglement production. An optical parametric oscillator operating above threshold produces an inseparable state of pump, signal and idler modes. Previous attempts had been frustrated by the presence of an extra noise source, which is shown to be generated by photon scattering of light due to thermal phonons of the crystal. Reduction of this noise is achieved by cooling the KTP crystal of OPO down to -10deg C. Reflected pump field, signal and idler fields are measured after reflection by empty cavities (enabling the measurement of amplitude or phase quadrature) using efficient photodiodes, allowing the complete measurement of the covariance matrix. The photocurrent component at 21 MHz, used in the analysis, was registered with the help of an analog-to-digital card and a computer.

DOI
10.1109/cleoe-eqec.2009.5194550

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This paper demonstrates the nonlinear system of the smallest order for direct tripartite entanglement production. An optical parametric oscillator operating above threshold produces an inseparable state of pump, signal and idler modes. Previous attempts had been frustrated by the presence of an extra noise source, which is shown to be generated by photon scattering of light due to thermal phonons of the crystal. Reduction of this noise is achieved by cooling the KTP crystal of OPO down to -10deg C. Reflected pump field, signal and idler fields are measured after reflection by empty cavities (enabling the measurement of amplitude or phase quadrature) using efficient photodiodes, allowing the complete measurement of the covariance matrix. The photocurrent component at 21 MHz, used in the analysis, was registered with the help of an analog-to-digital card and a computer.
Recent experiments with optical parametric oscillators have shown that an unpredicted extra noise on the phase of the fields reduces the level of squeezing or quantum correlations. In some cases, it can hinder the attempts to observe entanglement in those systems. It is probably the main reason why signal and idler entanglement above threshold remained unobserved by almost 20 years after its prediction. This paper investigates that the extra noise can be explained by phonon scattering of the central carrier of the intense field. In this Brillouin process, the scattered light acts as an extra noise source in the sideband where squeezing is generally observed. With this model, the linear dependence of the excess noise with the intracavity power and its behavior with temperature can be explained. Adding this noise source to the analysis of the quantum features in the OPO above threshold, recent results in the quest for tripartite entanglement in the OPO above threshold can be explained.
We show theoretically and experimentally that scattered light by thermal phonons inside a second-order nonlinear crystal is the source of additional phase noise observed in optical parametric oscillators. This additional phase noise reduces the quantum correlations and has hitherto hindered the direct production of multipartite entanglement in a single nonlinear optical system. We cooled the nonlinear crystal and observed a reduction in the extra noise. Our treatment of this noise can be successfully applied to different systems in the literature.
We calculate the quantum correlations existing among the three output fields (pump, signal, and idler) of a triply resonant nondegenerate optical parametric oscillator operating above threshold. By applying the standard criteria [P. van Loock and A. Furusawa, Phys. Rev. A 67, 052315 (2003)], we show that strong tripartite continuous-variable entanglement is present in this well-known and simple system. Furthermore, since the entanglement is generated directly from a nonlinear process, the three entangled fields can have very different frequencies, opening the way for multicolored quantum information networks.
The quantum correlations between the output signal, the output idler and the reflected pump fields generated by non-degenerate optical parametric oscillator operating above the oscillation threshold are theoretically calculated with the semi-classical formulae. According to the multipartite entanglement criteria for the continuous variables, proposed by P. van Loock and A. Furusawa, the calculated results prove the existence of the quantum correlations between the amplitude and the phase quadrature for the three optical fields, i. e. they form a tripartite entangled state. We numerically calculate the dependence of the entanglement on the physical parameters of the optical oscillator and find the optimum operating conditions of the oscillator to produce the three-color tripartite entangled state, which provide the direct references for the design of the continuous variable multipartite entanglement generation systems.
We have constructed a mode-locked optical parametric oscillator (OPO), synchronously pumped by the second harmonic of a continuously mode-locked Nd:YAG laser and based on type II phase matching in a KTP crystal. The two subharmonics (signal and idler waves) are nearly degenerate in frequency but are distinct orthogonal polarization states, and the oscillator is thus a nondegenerate OPO. Above threshold, the intensities of the signal and idler output beams should be highly correlated, as recently demonstrated for a similar single-frequency OPO.1 Ideally, the quantum noise on the corresponding photocurrent difference signal is completely suppressed for frequencies that are small compared to the OPO cavity bandwidth. Since this configuration produces intense light beams with potentially very good noise suppression, it is an important prototype for possible applications, e.g., to spectroscopy. Initial results with our OPO show an excess uncorrelated polarization noise, possibly due to depolarized light scattering in the KTP crystal. When the OPO cavity is stabilized with the signal and idler degenerate in frequency, they can be mixed to form a superposition by manipulating their polarization. When the oscillator is pumped below threshold, a pulsed squeezed vacuum state is produced in two such mixtures.2 When the polarizations are mixed inside the OPO cavity by a Faraday rotator, the backaction evasion necessary for a quantum nondemolition (QND) measurement of one of the field quadratures of an externally injected beam is obtained.3 The pulsed local oscillator used in observing the squeezing or QND effects is derived from the fundamental output of the pump laser. Progress in implementing these experiments with our mode-locked OPO is described as well as possible applications to time-domain measurements with noise below the shot-noise limit.